Title

Solving the Schrödinger   equation without the variational method: no integrals

Reporter

Prof. Tucker Carrington

Reporter’s   institution

Chemistry Department,   Queen's University, Kingston, Canada

Report time

2019-05-24 15:00

Report location

Science and Technology Exhibition Hall on   the 1st floor of Hefei National Laboratory for Physical Sciences at the   Microscale

Organizer

Hefei National Laboratory for Physical   Sciences at the Microscale, International Center for Chemical Theory (ICCT)

Report introduction

Abstract:

When the potential energy surface (PES) does   not have a special form (e.g. a sum of products), it is common to use   quadrature to compute a vibrational spectrum. Direct-product quadrature grids   are most popular. The size of a direct-product grid scales exponentially with   the number of atoms and it is not not possible to store values of the PES for   molecules with more than 5 atoms. In this talk, I shall present collocation   methods we are developing. Collocation has advantages: 1) point selection is   less important; 2) no integrals, no quadratures, no weights; 3) easy to use   with complicated kinetic energy operators; 4) it can be used with any (the   best possible) coordinates and basis functions; 5) in many cases fewer   collocation than quadrature points are required; 6) the length of the vectors   one must store is reduced. Collocation can be used with the   Multi-configuration Time-Dependent Hartree (MCTDH) approach. The   collocation-based MCTDH method I shall present can be used with general   potential energy surfaces. This is imperative if one wishes to compute very   accurate spectra. When the basis is good, the accuracy of collocation   solutions to the Schrödinger equation is not sensitive to the choice of the   collocation points. The original collocation-MCTDH (C-MCTDH) method [J. Chem.   Phys. 148, 044115 (2018)] uses, as is also true in standard MCTDH, a direct   product basis. Because we do not rely on having a sum-of-products potential   energy surface, we also have a direct product grid. By using generalized   hierarchical basis functions, that span the same space as the single particle   functions we introduced in the first C-MCTDH paper, and a Smolyak grid, we   have developed C-MCTDH approach that makes it possible to prune both the   basis and the grid.

Biosketch:

Prof.   Tucker Carrington has been focusing on developing new methods to study   quantum dynamics and spectroscopy. He received Diploma at University of   Toronto in 1981, and Ph. D degree at University of California at Berkeley in   1985. After that, he became a Research Fellow and Associate Professor at   Department of Chemistry - University de Montreal from 1988 to 1998. He   became a full Professor at Department of Chemistry - University de   Montreal in 1998. He has been a Canada Research Chair (Tier I) in Computational   Quantum Dynamics at Queen's University since 2007. He is a Fellow of American   Physical Society and Chemical Institute of Canada. He received many awards,   including recent prestigious ones such as, Alexander von Humboldt Research   Award (2017), John C. Polanyi Award of the Canadian Society for Chemistry   (2014), Gerhard Herzberg award of the Canadian Society for Analytical   Sciences and Spectroscopy (2013). He is the Member of the Editorial Board of   Molecular Physics and Associate Editor of the Journal of Theoretical and   Computational Chemistry.